Computer Algebra System

Fermat — A computer algebra system that does arithmetic of arbitrarily long integers and fractions, multivariate polynomials, symbolic calculations, matrices over polynomial rings, graphics, and other numerical calculations.

FreeMat — A Matlab-like program that supports many of its functions and features a codeless interface to external C, C++, and Fortran code, further parallel distributed algorithm development (via MPI), and 3D visualization capabilities.

Molecular Modeling

Quantum Espresso — integrated suite of computer codes for electronic-structure calculations and materials modeling at the nanoscale. It is based on density-functional theory, plane waves, and pseudopotentials (both norm-conserving and ultrasoft)